Ask the editor, but I would suggest to use the reviewer's proof. 

You say that will make you feel uncomfortable because you didn't make the most important contribution to the paper. This isn't necessarily true. First of all, you wrote the paper. Without you, there wouldn't have been any proofs to improve upon. Secondly, you do not know how the reviewer came up with their proof. Perhaps something they read in your paper gave them this idea. Perhaps not. We don't know, so try not to make any assumptions in that regard. They shared the proof with you, put something in the acknowledgements to recognize their contribution.